Question

which of the following is the equation of the line graphed below?
$\bigcirc y=-3x$
$\bigcirc y=3x-2$
$\bigcirc y=2x-3$
$\bigcirc y=-3x+2$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 2)$, so $b=2$.

Step2: Calculate slope

Pick two points: $(0,2)$ and $(1,-1)$. Slope $m=\frac{-1-2}{1-0}=-3$.

Step3: Write line equation

Use slope-intercept form $y=mx+b$. Substitute $m=-3$, $b=2$.
$y=-3x+2$

Step4: Match with options

Compare to given choices, matches the last option.

Answer:

D. $y=-3x+2$